DSpace at VNU: First Observation of the Decay B (s2)(5840)(0) - B K-+(-) and Studies of Excited B-s(0) Mesons

PRL 110, 151803 (2013)

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PHYSICAL REVIEW LETTERS

First Observation of the Decay BÃs2 ð5840Þ0 ! BÃþ KÀ and Studies of Excited B0s Mesons
R. Aaij et al.*
(LHCb Collaboration)
(Received 27 November 2012; revised manuscript received 11 February 2013; published 9 April 2013)
The properties of the orbitally excited (L ¼ 1) B0s states are studied by using 1:0 fbÀ1 of pp collisions
pffiffiffi
at s ¼ 7 TeV collected with the LHCb detector. The first observation of the BÃs2 ð5840Þ0 meson decaying
to BÃþ K À is reported, and the corresponding branching fraction measured relative to the Bþ KÀ decay
mode. The Bs1 ð5830Þ0 ! BÃþ K À decay is observed as well. The width of the BÃs2 ð5840Þ0 state is
measured for the first time, and the masses of the two states are determined with the highest precision
to date. The observation of the BÃs2 ð5840Þ0 ! BÃþ K À decay favors the spin-parity assignment J P ¼ 2þ
for the BÃs2 ð5840Þ0 meson. In addition, the most precise measurement of the mass difference
mðBÃþ Þ À mðBþ Þ ¼ 45:01 Æ 0:30ðstatÞ Æ 0:23ðsystÞ MeV=c2 is obtained.
DOI: 10.1103/PhysRevLett.110.151803

PACS numbers: 13.25.Hw, 12.39.Hg, 14.40.Nd

Heavy quark effective theory describes mesons with one
heavy and one light quark where the heavy quark is
assumed to have infinite mass [1]. It is an important tool
for calculating meson properties which may be modified
by physics beyond the standard model, such as CP violation in charm meson decays [2] or the mixing and lifetimes
of B mesons [3]. It also predicts the properties of excited B
and B0s mesons [4–7], and precise measurements of these

properties are a sensitive test of the validity of the theory.
Within heavy quark effective theory the B0s mesons are
characterized by three quantum numbers: the relative orbital angular momentum L of the two quarks, the total
angular momentum of the light quark jq ¼ jL Æ 12 j, and
the total angular momentum of the B0s meson J ¼ jjq Æ 12 j.
For L ¼ 1 there are four different possible (J, jq ) combinations, all with even parity. These are collectively termed
the orbitally excited states. Such states can decay to Bþ KÀ
and/or BÃþ KÀ (the inclusion of charge-conjugate states is
implied throughout this Letter), depending on their quantum numbers and mass values. The two states with jq ¼
1=2, named BÃs0 and B0s1 , are expected to decay through an
S-wave transition and to have a large Oð100 MeV=c2 Þ
decay width. In contrast, the two states with jq ¼ 3=2,
named Bs1 ð5830Þ0 and BÃs2 ð5840Þ0 (henceforth Bs1 and
BÃs2 for brevity), are expected to decay through a D-wave
transition and to have a narrow Oð1 MeV=c2 Þ decay width.
Table I gives an overview of these states.
In this Letter, a 1:0 fbÀ1 sample of data collected
by the LHCb detector is used to search for the orbitally
excited B0s mesons in the mass distribution of Bþ KÀ pairs,
where the Bþ mesons are selected in the four decay modes:
*Full author list given at the end of the article.
Published by the American Physical Society under the terms of
the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and
the published article’s title, journal citation, and DOI.

0031-9007=13=110(15)=151803(9)

Bþ ! J= c ðþ À ÞKþ , Bþ ! D" 0 ðK þ À Þþ , Bþ !
D" 0 ðK þ À þ À Þþ , and Bþ ! D" 0 ðK þ À Þþ À þ .
Two narrow peaks were observed in the Bþ KÀ mass

distribution by the CDF Collaboration [9]. Putatively,
they are identified with the states of the jq ¼ 3=2 doublet
expected in heavy quark effective theory [4] and are named
Bs1 and BÃs2 . As the Bs1 ! Bþ KÀ decay is forbidden, one
of the mass peaks observed is interpreted as the Bs1 !
BÃþ K À decay followed by BÃþ ! Bþ
, where the photon
is not observed. This peak is shifted by the BÃþ À Bþ mass
difference due to the missing momentum of the photon in
the BÃþ ! Bþ
decay. While the BÃs2 ! Bþ KÀ decay has
been observed by the D0 Collaboration as well [10], a
confirmation of the Bs1 meson is still missing. The identification of the Bs1 and BÃs2 mesons in the Bþ KÀ mass
spectrum is based on the expected mass splitting between
the jq ¼ 3=2 states. The Bs1 and BÃs2 widths are very
sensitive to their masses, due to their proximity to the
BK and BÃ K thresholds. Measurements of the widths
thus provide fundamental information concerning the
nature of these states. In addition, the Bs1 and BÃs2 quantum
numbers have not yet been directly determined, and the
observation of other decay modes can constrain the spinparity combinations of the states. In particular, the BÃs2 !
BÃþ K À decay has not yet been observed but could manifest
itself in the Bþ KÀ mass spectrum in a similar fashion to
the corresponding Bs1 meson decay. The BÃs2 ! BÃþ KÀ
branching fraction relative to BÃs2 ! Bþ KÀ is predicted to
TABLE I. Summary of the orbitally excited (L ¼ 1) B0s states.

BÃs0
B0s1
Bs1

BÃs2

151803-1

jq

JP

1=2
1=2
3=2
3=2

0þ
1þ
1þ
2þ

Allowed decay mode
Bþ K À
BÃþ K À
Yes
No
No
Yes

No
Yes
Yes
Yes

Mass (MeV=c2 ) [8]
Unobserved
Unobserved
5829:4 Æ 0:7
5839:7 Æ 0:6

Ó 2013 CERN, for the LHCb Collaboration


PRL 110, 151803 (2013)

PHYSICAL REVIEW LETTERS

be between 2% and 10%, depending on the BÃs2 mass
[11–14].
Recently, the Belle Collaboration has reported
observation of charged bottomoniumlike Zb ð10610Þþ and
Zb ð10650Þþ states [15,16] that could be interpreted as BB" Ã
and BÃ B" Ã molecules, respectively [17]. To test this interpretation, improved measurements of the BÃþ mass are
necessary and can be obtained from the difference in
peak positions between BÃs2 ! BÃþ KÀ and BÃs2 ! Bþ KÀ
decays in the Bþ KÀ mass spectrum.
The LHCb detector [18] is a single-arm forward spectrometer covering the pseudorapidity range 2 <  < 5,
designed for studying particles containing b or c quarks.
The detector includes a high-precision tracking system
consisting of a silicon-strip vertex detector surrounding
the pp interaction region, a large-area silicon-strip detector
located upstream of a dipole magnet with a bending power
of about 4 Tm, and three stations of silicon-strip detectors

and straw drift tubes placed downstream. The combined
tracking system has a momentum resolution (Áp=p), that
varies from 0.4% at 5 GeV=c to 0.6% at 100 GeV=c, and a
decay time resolution of 50 fs. The resolution of the impact
parameter, the transverse distance of closest approach
between the track and a primary interaction, is about
20 m for tracks with large transverse momentum. The
transverse component is measured in the plane normal to
the beam axis. Charged hadrons are identified by using two
ring-imaging Cherenkov detectors. Photon, electron, and
hadron candidates are identified by a calorimeter system
consisting of scintillating-pad and preshower detectors, an
electromagnetic calorimeter, and a hadronic calorimeter.
Muons are identified by a system composed of alternating
layers of iron and multiwire proportional chambers.
The trigger system [19] consists of a hardware stage,
based on information from the calorimeter and muon systems, followed by a software stage that applies a full event
reconstruction. Events likely to contain a B meson are
selected by searching for a dimuon vertex detached from
the primary interaction or two-, three-, and four-track
vertices detached from the primary interaction which
have high total transverse momentum. These are, respectively, referred to as dimuon and topological triggers.
The samples of simulated events used in this analysis are
based on the PYTHIA 6.4 generator [20], with a choice of
parameters specifically configured for LHCb [21]. The
EVTGEN package [22] describes the decay of the B mesons,
and the GEANT4 toolkit [23,24] is used to simulate the
detector response. QED radiative corrections are generated
with the PHOTOS package [25].
In the offline analysis the B mesons are reconstructed by

using a set of loose selection criteria to suppress the
majority of the combinatorial backgrounds. The Bþ !
J= c Kþ selection requires a Bþ candidate with a transverse
momentum of at least 2 GeV=c and a decay time of at least
0.3 ps. For the other decay modes, the selection explicitly

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requires that the topological trigger, which selected the
event, is based exclusively on tracks from which the B
meson candidate is formed. Additional loose selection
requirements are placed on variables related to the B meson
production and decay such as transverse momentum and
quality of the track fits for the decay products, detachment
of the Bþ candidate from the primary interaction, whether
the momentum of the Bþ candidate points back to the
primary interaction, and the impact parameter 2 . The
impact parameter 2 is defined as the difference between
the 2 of the primary vertex reconstructed with and without the considered track.
Following these selections, Bþ signals are visible above
backgrounds in all four decay modes. In order to improve
their purity, four boosted decision tree classifiers [26] are
trained on variables common to all four decay modes: the
transverse momenta and impact parameters of the final
state tracks, the transverse momentum and impact parameter of the Bþ candidate, the detachment of the Bþ candidate from the primary interaction, the cosine of the angle
between the Bþ candidate momentum and the direction of
flight from the primary vertex to the decay vertex, the fit 2
of the tracks, and particle identification information. The
classifier is trained on data by using the sWeights technique

[27], with the Bþ candidate mass as a discriminating
variable, to unfold the signal and background distributions.
The cut on the classifier response is chosen by optimizing
the significance of each Bþ signal. The final mass distributions for the Bþ candidates are shown in Fig. 1.
The Bþ candidate mass spectra are fitted by using a
double Gaussian function for the signal and a second-order
polynomial for the background. The average mass resolution Bþ is defined as the weighted average of the Gaussian
widths. The purities of the samples, defined as the fraction
of the signal events in a Æ2Bþ mass region, are 96%,
91%, 90%, and 85% for the Bþ ! J= c Kþ , Bþ !
D" 0 ðK þ À Þþ , Bþ ! D" 0 ðKþ À þ À Þþ , and Bþ !
D" 0 ðK þ À Þþ À þ decays, respectively. The Bþ candidates, within a Æ2Bþ mass region, are selected for each
decay mode. A sample of about 1000000 Bþ candidates is
obtained and combined with any track of opposite charge
that is identified as a kaon.
Multiple pp interactions can occur in LHC bunch crossings. In order to reduce combinatorial backgrounds, the Bþ
and kaon candidates are required to be consistent with
coming from the same interaction point. The signal purity
is improved by a boosted decision tree classifier, whose
inputs are the Bþ and the kaon transverse momenta, the
log-likelihood difference between the kaon and pion
hypotheses, and the vertex fit and impact parameter 2 .
The training is performed by using simulated events for
the signal and the like-charge Bþ K þ candidates in the data
for the background. The same selection is subsequently
applied to all Bþ decay modes. The cut on the classifier
response is chosen by optimizing the significance of the

151803-2

15000
10000
5000
0

6000

3500

(b)

LHCb

5000
4000
3000
2000
1000

5200 5250 5300 5350
+
+
m(J/ψ (µ µ-)K ) [MeV/c2]

0

3000

(c)

LHCb

2500
2000
1500
1000

5200 5250 5300 5350
m(D0(K+π-)π+) [MeV/c2]

500
0

5200 5250 5300 5350

m(D0(K+π-π+π-)π+) [MeV/c2]

Candidates / (1 MeV/c2)

LHCb

Candidates / (1 MeV/c2)

(a)

Candidates / (1 MeV/c2)

Candidates / (1 MeV/c2)

20000

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PHYSICAL REVIEW LETTERS

PRL 110, 151803 (2013)

1800
1600
1400
1200
1000
800
600
400
200
0

(d)

LHCb

5200 5250 5300 5350

m(D0(K+π-)π+π-π+) [MeV/c2]

FIG. 1 (color online). Invariant mass spectra of the final Bþ candidates. The signal line shape is fitted with a double Gaussian
distribution, while the background is modeled with a second-order polynomial. (a) Bþ ! J= c K þ , (b) Bþ ! D" 0 ðK þ À Þþ ,

(c) Bþ ! D" 0 ðK þ À þ À Þþ , and (d) Bþ ! D" 0 ðK þ À Þþ À þ decays. The J= c and D0 masses are constrained to their world
average values.

BÃs2 ! Bþ KÀ signal. It retains 57% of the signal events
and rejects 92% of the background events. In order to
improve the mass resolution, the Bþ KÀ mass fits are
performed by constraining the J= c (or D0 ) and Bþ particles to their respective world average masses [8] and
constraining the Bþ and KÀ momenta to point to the
associated primary vertex.
Figure 2 shows the mass difference for the selected
candidates, summed over all Bþ decay modes. The mass
difference is defined as Q  mðBþ KÀ Þ À mðBþ Þ À
mðKÀ Þ, where mðBþ Þ and mðK À Þ are the known masses
of the Bþ and KÀ mesons [8], respectively. The two narrow
peaks at 10 and 67 MeV=c2 are identified as the Bs1 !
BÃþ KÀ and BÃs2 ! Bþ K À signals, respectively, as previously observed. In addition, a smaller structure is seen
around 20 MeV=c2 , identified as the previously unobserved BÃs2 ! BÃþ KÀ decay mode.
Simulated events are used to compute the detector resolutions corresponding to the three signals. The values
obtained are increased by 20% to account for differences

Pull

Candidates / (1 MeV/c2)

1000

-

LHCb

800

Bs1 → B*+K

600
400

-

B*s2 → B*+K

-

B*s2 → B+K 500
400
300
200
100
0
0

5

10 15 20 25 30 35

200

0
2
-2

0

20

40

60
80 100 120 140 160
m(B+K ) - m(B+) - m(K ) [MeV/c2]

180

200

FIG. 2 (color online). Mass difference distribution
mðBþ K À Þ À mðBþ Þ À mðK À Þ. The three peaks are identified
as (left) Bs1 ! BÃþ K À , (middle) BÃs2 ! BÃþ K À , and (right)
BÃs2 ! Bþ K À . The total fit function is shown as a solid blue
line, while the shaded red region is the spectrum of like-charge
Bþ K þ combinations. The inset shows an expanded view of the
Bs1 =BÃs2 ! BÃþ K À signals. The bottom plot shows the fit pulls.

between the Bþ resolutions in data and simulated events.
The corrected resolutions are 0.4, 0.6, and 1:0 MeV=c2 for
the Bs1 ! BÃþ K À , BÃs2 ! BÃþ K À , and BÃs2 ! Bþ KÀ signals, respectively. A discrepancy of 40% between the mass
resolutions in data and simulated events is observed for
decays with small Q values, such as DÃþ ! D0 þ .
Therefore we assign an uncertainty of Æ20% to the resolution in the systematic studies.
An unbinned fit of the mass difference distribution is
performed to extract the Q values and event yields of the

three peaks. The BÃs2 ! Bþ KÀ signal is parameterized by a
relativistic Breit-Wigner function with natural width À
convolved with a Gaussian function that accounts for the
detector resolution. Its width is fixed to the value obtained
from simulated events. The line shapes of the Bs1 =BÃs2 !
BÃþ K À signals, expected to be Breit-Wigner functions in
the BÃþ KÀ mass spectrum, are affected by the phase space
and the angular distribution of the decays, as the photon is
not reconstructed. The resulting shapes cannot be properly
simulated due to the lack of knowledge of the Bs1 =BÃs2
properties. Therefore, a Gaussian function is used for
each Bs1 =BÃs2 ! BÃþ K À signal as effective parameterization. The background is modeled by a threshold function fðQÞ ¼ Q e
Qþ , where ,
, and  are free
parameters in the fit. Its analytical form is verified by
fitting the like-charge Bþ Kþ combinations where no
signal is expected.
The parameters allowed to vary in the fit are the yield
NBÃs2 !Bþ KÀ , the yield ratios NBs1 !BÃþ KÀ =NBÃs2 !Bþ KÀ and
NBÃs2 !BÃþ KÀ =NBÃs2 !Bþ KÀ , the Q values of the Bs1 !
BÃþ K À and BÃs2 ! Bþ KÀ signals, the mass difference
between the BÃs2 ! Bþ K À and BÃs2 ! BÃþ KÀ peaks, the
natural width of the BÃs2 state, the Gaussian widths of
Bs1 =BÃs2 ! BÃþ KÀ signals, and the parameters of the
threshold function. From the yield ratios, the relative
branching fraction

151803-3

NBÃ !BÃþ KÀ

BðBÃs2 ! BÃþ KÀ Þ
BÃs2
¼ s2
 rel
2;2 ¼ R
Ã
þ
À
BðBs2 ! B K Þ
NBÃs2 !Bþ KÀ

(1)


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PHYSICAL REVIEW LETTERS

PRL 110, 151803 (2013)

TABLE II. Results of the fit to the mass difference distributions mðBþ K À Þ À mðBþ Þ À
mðK À Þ. The first uncertainties are statistical, and the second are systematic.
Parameter

Fit result
mðBÃþ Þ

mðK À Þ

À
mðBs1 Þ À
mðBÃs2 Þ À mðBþ Þ À mðK À Þ
mðBÃþ Þ À mðBþ Þ
ÀðBÃs2 Þ
BðBÃs2 !BÃþ KÀ Þ
BðBÃs2 !Bþ KÀ Þ
ðpp!Bs1 XÞBðBs1 !BÃþ KÀ Þ
ðpp!BÃs2 XÞBðBÃs2 !Bþ KÀ Þ

Best previous measurement
MeV=c2

10:46 Æ 0:04 Æ 0:04
10:73 Æ 0:21 Æ 0:14 MeV=c2 [9]
2
67:06 Æ 0:05 Æ 0:11 MeV=c 66:96 Æ 0:39 Æ 0:14 MeV=c2 [9]
45:01 Æ 0:30 Æ 0:23 MeV=c2
45:6 Æ 0:8 MeV=c2 [28]
2
1:56 Æ 0:13 Æ 0:47 MeV=c
ð9:3 Æ 1:3 Æ 1:2Þ%
ð23:2 Æ 1:4 Æ 1:3Þ%
750 Æ 36
307 Æ 46
3140 Æ 100

NBs1
NBÃs2 !BÃþ KÀ
NBÃs2 !Bþ KÀ

!BÃþ KÀ

is measured. The Bs1 to BÃs2 ratio of production cross
sections times the ratio of branching fractions of Bs1 !
BÃþ KÀ relative to that of BÃs2 ! Bþ KÀ is also determined
from
ðpp ! Bs1 XÞBðBs1 ! BÃþ KÀ Þ
ðpp ! BÃs2 XÞBðBÃs2 ! Bþ K À Þ
NB !BÃþ KÀ
Bs1 =BÃs2 Bs1 =BÃs2
 rel
R
:
¼ s1
1;2 ¼ 
NBÃs2 !Bþ KÀ

(2)

These ratios are corrected by the relative selection efficienrel
cies rel
2;2 ¼ 1:05 Æ 0:02 and 1;2 ¼ 1:03 Æ 0:01, using
simulated decays. The fit results are given in Table II.
The widths of the two Gaussian functions are 0:73 Æ
0:04 and 1:9 Æ 0:3 MeV=c2 for the Bs1 ! BÃþ K À and
BÃs2 ! BÃþ KÀ signals, respectively. A binned 2 test gives
a confidence level of 43% for the fit.
To determine the significance of the BÃs2 ! BÃþ KÀ signal, a similar maximum likelihood fit is performed, where
all parameters of the signal are fixed according to expectation, except its yield. The likelihood of this fit is compared to the result of a fit where the yield of the signal is
fixed to zero. The statistical significance of the BÃs2 !

BÃþ KÀ signal is 8.
A number of systematic uncertainties are considered.
For the signal model, the signal shape is changed to a

double Gaussian function and an alternative threshold
function is used for the background. The changes in the
fit results are assigned as the associated uncertainties. The
Bþ decay modes are fitted independently to test for effects
that may be related to differences in their selection requirements. For each observable quoted in Table II, the difference between the weighted average of these independent
fits and the global fit is taken as a systematic uncertainty.
Additional systematic uncertainties are assigned based on
the change in the results when varying the selection criteria
and the Bþ signal region. The detector resolution of BÃs2 !
Bþ KÀ signal is varied by Æ20%. In addition, the momentum scale in the processing of the data used in this analysis
is varied within the estimated uncertainty of 0.15%. The
corresponding uncertainty on the measured masses is
assigned as a systematic uncertainty. The uncertainty on
the determination of the selection efficiency ratios caused
by finite samples of simulated events is taken as a systematic uncertainty for the branching fractions. Finally, simulated events are used to estimate the mass shifts of the
Bs1 =BÃs2 ! BÃþ KÀ signals from the nominal values when
the radiated photon is excluded from their reconstructed
decays. The absolute systematic uncertainties are given
in Table III. The BÃs2 ! BÃþ KÀ signal is observed with
the expected frequency in each of the four resconstructed

TABLE III. Absolute systematic uncertainties for each measurement, which are assumed to be
independent and are added in quadrature.
Ã

Source

Fit model
Bþ decay mode
Selection
Bþ signal region
Mass resolution
Momentum scale
Efficiency ratios
Missing photon
Total

Ã

Ã

QðBs1 Þ
QðBÃs2 Þ mðBÃþ Þ À mðBþ Þ ÀðBÃs2 Þ RBs2 Bs1 =Bs2 RBs1 =Bs2
(%)
(MeV=c2 ) (MeV=c2 )
(MeV=c2 )
(MeV=c2 ) (%)
0.00
0.01
0.03
0.01
0.00
0.02
ÁÁÁ
0.01
0.04

0.02
0.01
0.02
0.03
0.01
0.10
ÁÁÁ
ÁÁÁ
0.11

0.03
0.02
0.19
0.11
0.02
0.03
ÁÁÁ
0.01
0.23

151803-4

0.01
0.01
0.05
0.07
0.46
ÁÁÁ
ÁÁÁ
ÁÁÁ

0.47

0.2
0.1
1.1
0.2
0.2
ÁÁÁ
0.2
ÁÁÁ
1.2

0.5
0.1
0.6
0.4
0.9
ÁÁÁ
0.2
ÁÁÁ
1.3


PRL 110, 151803 (2013)

PHYSICAL REVIEW LETTERS

decay modes, and the systematic error for the

BðBÃs2 !BÃþ K À Þ

BðBÃs2 !Bþ K À Þ
þ

branching fraction ratio, related to the different B decay
modes, is small. The final results are shown in Table II. The
measured mass differences are more precise than the previous best measurements of a factor of 2 at least. The
BðBÃ !BÃþ K À Þ
measured BðBs2Ã !Bþ KÀ Þ branching fraction ratio and BÃs2
s2

width are in good agreement with theoretical predictions
[12–14].
The mass differences given in Table II are translated into
absolute masses by adding the masses of the Bþ and kaon
[8] and, in the case of the Bs1 meson, the BÃþ À Bþ mass
difference measured in this Letter. The results are
mðBÃþ Þ ¼ 5324:26 Æ 0:30 Æ 0:23 Æ 0:17 MeV=c2 ;
mðBs1 Þ ¼ 5828:40 Æ 0:04 Æ 0:04 Æ 0:41 MeV=c2 ;
mðBÃs2 Þ ¼ 5839:99 Æ 0:05 Æ 0:11 Æ 0:17 MeV=c2 ;
where the first uncertainty is statistical and the second is
systematic. The third uncertainty corresponds to the uncertainty on the Bþ mass [8] and, in the case of the Bs1 mass
measurement, the uncertainty on the BÃþ À Bþ mass difference measured in this analysis.
The significance of the nonzero BÃs2 width is determined
by comparing the likelihood for the nominal fit with a fit in
which the width is fixed to zero. To account for systematic
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
effects, the minimum 2Á logL among all systematic
variations is taken; the significance including systematic
uncertainties is 9.
À1

In conclusion, by using
pffiffiffi 1:0 fb of data collected Ãwith
the LHCb detector at s ¼ 7 TeV, the decay mode Bs2 !
BÃþ KÀ is observed for the first time and its branching
fraction measured relative to that of BÃs2 ! Bþ KÀ . The
observation of the BÃs2 meson decaying to two pseudoscalars (BÃs2 ! Bþ KÀ ) and to a vector and a pseudoscalar
(BÃs2 ! BÃþ KÀ ) favors the assignment of J P ¼ 2þ for
this state. The BÃs2 width is measured for the first time,
while the masses of the Bs1 and BÃs2 states are measured
with the highest precision to date and are consistent with
previous measurements [9,10]. Finally, the observed
BÃs2 ! BÃþ KÀ decay is used to make the most precise
measurement to date of the BÃþ À Bþ mass difference.
This measurement, unlike others reported in the literature,
does not require the reconstruction of the soft photon from
BÃþ decays and therefore has significantly smaller systematic uncertainty. High precision measurements of the BÃþ
mass are important for the understanding of the exotic Zþ
b
states recently observed [15]. Using the BÃþ mass measured in this analysis, we compute that the Zb ð10610Þþ and
Zb ð10650Þþ masses are 3:69 Æ 2:05 and 3:68 Æ
1:71 MeV=c2 above the BB" Ã and BÃ B" Ã thresholds,
respectively.
We express our gratitude to our colleagues in the CERN
accelerator departments for the excellent performance of
the LHC. We thank the technical and administrative staff at

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the LHCb institutes. We acknowledge support from CERN

and from the national agencies: CAPES, CNPq, FAPERJ,
and FINEP (Brazil); NSFC (China); CNRS/IN2P3 and
Region Auvergne (France); BMBF, DFG, HGF, and
MPG (Germany); SFI (Ireland); INFN (Italy); FOM
and NWO (Netherlands); SCSR (Poland); ANCS/IFA
(Romania); MinES, Rosatom, RFBR, and NRC
‘‘Kurchatov Institute’’ (Russia); MinECo, XuntaGal, and
GENCAT (Spain); SNSF and SER (Switzerland); NAS
Ukraine (Ukraine); STFC (United Kingdom); NSF
(USA). We also acknowledge the support received from
the ERC under FP7. The Tier1 computing centres are
supported by IN2P3 (France), KIT and BMBF
(Germany), INFN (Italy), NWO and SURF
(Netherlands), PIC (Spain), and GridPP (United
Kingdom). We are thankful for the computing resources
put at our disposal by Yandex LLC (Russia), as well as to
the communities behind the multiple open source software
packages that we depend on.

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C. Lazzeroni,42 R. Le Gac,6 J. van Leerdam,38 J.-P. Lees,4 R. Lefe`vre,5 A. Leflat,29 J. Lefranc¸ois,7 O. Leroy,6
T. Lesiak,23 Y. Li,3 L. Li Gioi,5 M. Liles,49 R. Lindner,35 C. Linn,11 B. Liu,3 G. Liu,35 J. von Loeben,20 J. H. Lopes,2
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I. V. Machikhiliyan,4,28 F. Maciuc,26 O. Maev,27,35 J. Magnin,1 M. Maino,20 S. Malde,52 G. Manca,15,d
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S. Oggero,38 S. Ogilvy,48 O. Okhrimenko,41 R. Oldeman,15,d M. Orlandea,26 J. M. Otalora Goicochea,2 P. Owen,50
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A. C. dos Reis,1 S. Ricciardi,46 A. Richards,50 K. Rinnert,49 V. Rives Molina,33 D. A. Roa Romero,5 P. Robbe,7
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E. Santovetti,21,k M. Sapunov,6 A. Sarti,18,l C. Satriano,22,m A. Satta,21 M. Savrie,16,e D. Savrina,28,29 P. Schaack,50
M. Schiller,39 H. Schindler,35 S. Schleich,9 M. Schlupp,9 M. Schmelling,10 B. Schmidt,35 O. Schneider,36
A. Schopper,35 M.-H. Schune,7 R. Schwemmer,35 B. Sciascia,18 A. Sciubba,18,l M. Seco,34 A. Semennikov,28
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T. Skwarnicki,53 N. A. Smith,49 E. Smith,52,46 M. Smith,51 K. Sobczak,5 F. J. P. Soler,48 F. Soomro,18 D. Souza,43
B. Souza De Paula,2 B. Spaan,9 A. Sparkes,47 P. Spradlin,48 F. Stagni,35 S. Stahl,11 O. Steinkamp,37 S. Stoica,26
S. Stone,53 B. Storaci,38 M. Straticiuc,26 U. Straumann,37 V. K. Subbiah,35 S. Swientek,9 V. Syropoulos,39
M. Szczekowski,25 P. Szczypka,36,35 T. Szumlak,24 S. T’Jampens,4 M. Teklishyn,7 E. Teodorescu,26 F. Teubert,35
C. Thomas,52 E. Thomas,35 J. van Tilburg,11 V. Tisserand,4 M. Tobin,37 S. Tolk,39 D. Tonelli,35 S. Topp-Joergensen,52
N. Torr,52 E. Tournefier,4,50 S. Tourneur,36 M. T. Tran,36 M. Tresch,37 A. Tsaregorodtsev,6 P. Tsopelas,38 N. Tuning,38
M. Ubeda Garcia,35 A. Ukleja,25 D. Urner,51 U. Uwer,11 V. Vagnoni,14 G. Valenti,14 R. Vazquez Gomez,33
P. Vazquez Regueiro,34 S. Vecchi,16 J. J. Velthuis,43 M. Veltri,17,g G. Veneziano,36 M. Vesterinen,35 B. Viaud,7
I. Videau,7 D. Vieira,2 X. Vilasis-Cardona,33,n J. Visniakov,34 A. Vollhardt,37 D. Volyanskyy,10 D. Voong,43
A. Vorobyev,27 V. Vorobyev,31 C. Voß,55 H. Voss,10 R. Waldi,55 R. Wallace,12 S. Wandernoth,11 J. Wang,53

D. R. Ward,44 N. K. Watson,42 A. D. Webber,51 D. Websdale,50 M. Whitehead,45 J. Wicht,35 D. Wiedner,11
L. Wiggers,38 G. Wilkinson,52 M. P. Williams,45,46 M. Williams,50,p F. F. Wilson,46 J. Wishahi,9 M. Witek,23
W. Witzeling,35 S. A. Wotton,44 S. Wright,44 S. Wu,3 K. Wyllie,35 Y. Xie,47,35 F. Xing,52 Z. Xing,53 Z. Yang,3
R. Young,47 X. Yuan,3 O. Yushchenko,32 M. Zangoli,14 M. Zavertyaev,10,a F. Zhang,3 L. Zhang,53 W. C. Zhang,12
Y. Zhang,3 A. Zhelezov,11 A. Zhokhov,28 L. Zhong,3 and A. Zvyagin35
(LHCb Collaboration)
1
2

Centro Brasileiro de Pesquisas Fı´sicas (CBPF), Rio de Janeiro, Brazil
Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3
Center for High Energy Physics, Tsinghua University, Beijing, China
4
LAPP, Universite´ de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France

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5

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12 APRIL 2013

Clermont Universite´, Universite´ Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France
6

CPPM, Aix-Marseille Universite´, CNRS/IN2P3, Marseille, France
7
LAL, Universite´ Paris-Sud, CNRS/IN2P3, Orsay, France
8
LPNHE, Universite´ Pierre et Marie Curie, Universite´ Paris Diderot, CNRS/IN2P3, Paris, France
9
Fakulta¨t Physik, Technische Universita¨t Dortmund, Dortmund, Germany
10
Max-Planck-Institut fu¨r Kernphysik (MPIK), Heidelberg, Germany
11
Physikalisches Institut, Ruprecht-Karls-Universita¨t Heidelberg, Heidelberg, Germany
12
School of Physics, University College Dublin, Dublin, Ireland
13
Sezione INFN di Bari, Bari, Italy
14
Sezione INFN di Bologna, Bologna, Italy
15
Sezione INFN di Cagliari, Cagliari, Italy
16
Sezione INFN di Ferrara, Ferrara, Italy
17
Sezione INFN di Firenze, Firenze, Italy
18
Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
19
Sezione INFN di Genova, Genova, Italy
20
Sezione INFN di Milano Bicocca, Milano, Italy
21

Sezione INFN di Roma Tor Vergata, Roma, Italy
22
Sezione INFN di Roma La Sapienza, Roma, Italy
23
Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Krako´w, Poland
24
Faculty of Physics and Applied Computer Science, AGH-University of Science and Technology, Krako´w, Poland
25
National Center for Nuclear Research (NCBJ), Warsaw, Poland
26
Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania
27
Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
28
Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
29
Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia
30
Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia
31
Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State University, Novosibirsk, Russia
32
Institute for High Energy Physics (IHEP), Protvino, Russia
33
Universitat de Barcelona, Barcelona, Spain
34
Universidad de Santiago de Compostela, Santiago de Compostela, Spain
35
European Organization for Nuclear Research (CERN), Geneva, Switzerland
36

Ecole Polytechnique Fe´de´rale de Lausanne (EPFL), Lausanne, Switzerland
37
Physik-Institut, Universita¨t Zu¨rich, Zu¨rich, Switzerland
38
Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
39
Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, The Netherlands
40
NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
41
Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine
42
University of Birmingham, Birmingham, United Kingdom
43
H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom
44
Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
45
Department of Physics, University of Warwick, Coventry, United Kingdom
46
STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
47
School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom
48
School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom
49
Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
50
Imperial College London, London, United Kingdom
51

School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom
52
Department of Physics, University of Oxford, Oxford, United Kingdom
53
Syracuse University, Syracuse, NY, United States
54
Pontifı´cia Universidade Cato´lica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil
(associated with Institution Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil)
55
Institut fu¨r Physik, Universita¨t Rostock, Rostock, Germany (associated with Institution Physikalisches Institut,
Ruprecht-Karls-Universita¨t Heidelberg, Heidelberg, Germany)
a

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P. N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia.
Universita` di Bari, Bari, Italy.
Universita` di Bologna, Bologna, Italy.
Universita` di Cagliari, Cagliari, Italy.
Universita` di Ferrara, Ferrara, Italy.
Universita` di Firenze, Firenze, Italy.

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PRL 110, 151803 (2013)
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PHYSICAL REVIEW LETTERS

Universita` di Urbino, Urbino, Italy.
Universita` di Modena e Reggio Emilia, Modena, Italy.
Universita` di Genova, Genova, Italy.
Universita` di Milano Bicocca, Milano, Italy.
Universita` di Roma Tor Vergata, Roma, Italy.
Universita` di Roma La Sapienza, Roma, Italy.
Universita` della Basilicata, Potenza, Italy.
LIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain.
Hanoi University of Science, Hanoi, Viet Nam.
Massachusetts Institute of Technology, Cambridge, MA, USA.

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